The analysis in this paper is based on the stereographic projection of the kinetic variable \(\theta \in \mathbb {S}^{d-1}\)  on the plane \(v\in \mathbb {R}^{d-1}\) , see [1]}. The benefit of such approach is the fact that the geometry of the kinetic space is replaced by Bessel weights which are manageable with Fourier methods and render explicit formulas for numerical implementation.
